# Thread: For each positive real number r, define T (subscript r)...

1. ## For each positive real number r, define T (subscript r)...

For each positive real number r, define T_r to be the closed interval [-r2,r2].
That is, T_r={x∈R|-r2≤x≤r2}.
Let indexing set = {m ∈ natural numbers |1≤m≤10}
Use either interval notation or set builder notation to specify each of the following sets:
⋃_(r∈R (+)) Tr
⋂_(r∈R (+)) Tr
⋃_(k∈natural numbers) Tk
⋂_(k∈natural numbers) Tk

The uppercase U is union, and upside down U is intersect. the Tr and Tk are supposed to be next to the symbol and the things in parenthesis are supposed to be below the symbol. I have no idea how to do these for problems can anyone help?

2. ## Re: For each positive real number r, define T (subscript r)...

Originally Posted by Brjakewa
For each positive real number r, define T_r to be the closed interval [-r2,r2].
That is, T_r={x∈R|-r2≤x≤r2}.
Let indexing set = {m ∈ natural numbers |1≤m≤10}
Use either interval notation or set builder notation to specify each of the following sets:
⋃_(r∈R (+)) Tr
⋂_(r∈R (+)) Tr
⋃_(k∈natural numbers) Tk
⋂_(k∈natural numbers) Tk
It is very hard to read the above quote.

Why not learn to post in symbols? You can use LaTeX tags

$$\bigcup\limits_{r \in \mathbb{R}^ + } {T_r }$$ gives $\displaystyle \bigcup\limits_{r \in \mathbb{R}^ + } {T_r }$
Of course the answer there is $\displaystyle \mathbb{R}$.

$\displaystyle \bigcap\limits_{r \in \mathbb{R}^ + } {T_r }=\{0\}$

3. ## Re: For each positive real number r, define T (subscript r)...

Thanks for your help, but the link you posted when clicked on says the page is not found? What about the other two cases (for the natural #'s) would the answers there be 0 to positive infinity for the union and empty set for intersect?

4. ## Re: For each positive real number r, define T (subscript r)...

Originally Posted by Brjakewa
Thanks for your help, but the link you posted when clicked on says the page is not found? What about the other two cases (for the natural #'s) would the answers there be 0 to positive infinity for the union and empty set for intersect?

5. ## Re: For each positive real number r, define T (subscript r)...

Again, could you help me out with the later two involving natural numbers?

6. ## Re: For each positive real number r, define T (subscript r)...

Originally Posted by Brjakewa
Again, could you help me out with the later two involving natural numbers?
The difficulty here is how one defines Natural Number.
There is no universal agreement on if zero is a natural number.

If $\displaystyle \mathbb{N}=\{1,2,3,\cdots\}$ then $\displaystyle \bigcap\limits_{n \in \mathbb{N}} {T_n } = \left[ { - 1,1} \right]$.

On the other hand, if $\displaystyle 0\in\mathbb{N}$ then $\displaystyle \bigcap\limits_{n \in \mathbb{N}} {T_n } = \{0\}$

In either case $\displaystyle \bigcup\limits_{n \in \mathbb{N}} {T_n } = \mathbb{R}$